The longest path in a random graph

Miklós Ajtai, János Komlós, Endre Szemerédi

Research output: Contribution to journalArticle

59 Citations (Scopus)


A random graph with (1+ε)n/2 edges contains a path of length cn. A random directed graph with (1+ε)n edges contains a directed path of length cn. This settles a conjecture of Erdõs.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
Issue number1
Publication statusPublished - Mar 1 1981


  • AMS subject classification (1980): 05C38, 60C05, 60J80

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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